Given that the initial rate constant is 0.0190s−1 at an initial temperature of 22 ∘C , what would the rate constant be at a temperature of 190 ∘C for the same reaction described in Part A?
Activation Energy 32.4kJ/mol
Use the Arrhenius equation. It should be 1.2
Post your work if you get stuck.
To determine the rate constant at a different temperature, we can use the Arrhenius equation, which relates the rate constant (k) to the activation energy (Ea) and temperature (T).
The Arrhenius equation is given by:
k = A * e^(-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor or frequency factor (constant)
- e is the base of the natural logarithm (approximately 2.71828)
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
To find the rate constant at a temperature of 190 °C, we need to convert this temperature to Kelvin:
T = 190 + 273.15 = 463.15 K
Now we can substitute the known values into the Arrhenius equation:
k1 = 0.0190 s^(-1) (initial rate constant)
T1 = 22 °C + 273.15 = 295.15 K (initial temperature)
Ea = 32.4 kJ/mol = 32,400 J/mol (activation energy)
R = 8.314 J/(mol·K) (gas constant)
T2 = 190 °C + 273.15 = 463.15 K (desired temperature)
Now we solve for k2, the rate constant at the desired temperature:
k2 = k1 * e^((Ea/R) * (1/T1 - 1/T2))
k2 = 0.0190 * e^((32,400 / 8.314) * (1/295.15 - 1/463.15))
Calculating this expression will give you the rate constant (k2) at a temperature of 190 °C.